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------------------------------------------------ The sum of 4.6 and one-third of a number is at most 39.1. What are all the possible values of the number?

Artem wrote the inequality [tex]\frac{1}{3}n + 4.6 \leq 39.1[/tex], where [tex]n[/tex] represents the number, to help solve this problem. Solve his inequality.

A. [tex]n \leq 112.7[/tex]
B. [tex]n \leq 11.5[/tex]
C. [tex]n \leq 131.1[/tex]
D. [tex]n \leq 103.5[/tex]

Sure! Let's solve the inequality step-by-step:

We are given the inequality:

[tex]\[
\frac{1}{3} n + 4.6 \leq 39.1
\][/tex]

and we need to find the possible values for the number [tex]\( n \)[/tex].

1. Subtract 4.6 from both sides:
To isolate the term with [tex]\( n \)[/tex], start by subtracting 4.6 from both sides:

[tex]\[
\frac{1}{3} n \leq 39.1 - 4.6
\][/tex]

2. Simplify the right side:
Perform the subtraction on the right side:

[tex]\[
\frac{1}{3} n \leq 34.5
\][/tex]

3. Solve for [tex]\( n \)[/tex]:
To solve for [tex]\( n \)[/tex], multiply both sides by 3 to get rid of the fraction:

[tex]\[
n \leq 34.5 \times 3
\][/tex]

4. Calculate the result:
Now calculate the multiplication:

[tex]\[
n \leq 103.5
\][/tex]

So, the possible values for the number [tex]\( n \)[/tex] are those that are less than or equal to 103.5. Therefore, the correct answer is [tex]\( n \leq 103.5 \)[/tex].